Approximation is an effective technique for reducing power consumption and latency of on-chip communication in many computing applications. However, existing approximation techniques either achieve modest improvements in these metrics or require retraining after approximation, such when convolutional neural networks (CNNs) are employed. Since classifying many images introduces intensive on-chip communication, reductions in both network latency and power consumption are highly desired. In this paper, we propose an approximate communication technique (ACT) to improve the efficiency of on-chip communications for image classification applications. The proposed technique exploits the error-tolerance of the image classification process to reduce power consumption and latency of on-chip communications, resulting in better overall performance for image classification computation. This is achieved by incorporating novel quality control and data approximation mechanisms that reduce the packet size. In particular, the proposed quality control mechanisms identify the error-resilient variables and automatically adjust the error thresholds of the variables based on the image classification accuracy. The proposed data approximation mechanisms significantly reduce packet size when the variables are transmitted. The proposed technique reduces the number of flits in each data packet as well as the on-chip communication, while maintaining an excellent image classification accuracy. The cycle-accurate simulation results show that ACT achieves 23% in network latency reduction and 24% in dynamic power reduction compared to the existing approximate communication technique with less than 0.99% classification accuracy loss.